It landed more like a lob than a smash, a proper surprise rather than a belting shock. No doubt Andy Murray will miss Ivan Lendl's inspirational presence in his player's box, chin planted motionlessly for hours on upturned palm, dark glasses under a baseball cap hiding his smart, still eyes, brain clocking every hit and miss. But he'll get over it.

When Lendl confirmed on Wednesday that he was walking away from the sport's most successful partnership of recent times – two grand slam titles and an Olympic gold medal in the two-and-a-bit years they were together – Murray was not devastated. They have been talking about breaking up "for a little while", I understand.

An insider described it as "like a relationship that had run its course, but the divorce was amicable". However, they have not seen each other since Murray lost to Roger Federer in the quarter-finals of the Australian Open, and Lendl might have been mildly concerned that Murray was embarking on a too-busy schedule, playing Acapulco for the first time as well as an exhibition in New York before the American hard-court swing. There was also his curious commitment to the end-of-season International Premier Tennis League in Asia, slap bang in the middle of his cherished winter training block in Miami.

Murray's next move will be to do his best this week in the Miami Open – where he defends the title and 1,000 ranking points – then return to Europe for a seriously slimmed-down clay programme. He will play Madrid, Rome and Roland Garros but misses Monte Carlo and has changed his mind about Estoril.

There is, I am told, no urgency about replacing Lendl – nor any obvious favourite for one of the most prized jobs in tennis. Darren Cahill, the astute Australian who travels extensively with ESPN and Adidas, might step in again temporarily, as he did in 2012 in the weird period between the sacking of Miles Maclagan and Alex Corretja, and Lendl's appointment before the 2012 Australian Open.

Murray also admires the philosophy of former world No 1 Mats Wilander, but the expatriate Swede spends most of the American summer doing small-town coaching clinics from the back of his Winnebago.

In the short (and long) term, the ever-present Dani Vallverdu, who has been with Murray as confidant and hitting partner since they were teenagers, will be there again. Murray's priority after leaving America will be Great Britain's Davis Cup tie against Italy in Naples next month, then an extended training block on clay, possibly in Barcelona, where he used to work with Corretja.

If his universe seems out of kilter, the split with Lendl left no bomb craters. The Czech was never hands-on. He often barked from afar. Murray happily took late-night, long-distance phone calls from him when he needed encouragement before a big match, and the respect and trust were mutual.

Lendl, not the most emotional of men, never disguised his admiration for Murray, even if he was not always there to witness his deeds first hand. Asked about Murray's struggle to rediscover his form since his back operation in September, Lendl said – while playing in an exhibition tournament in London – that he heard from Vallverdu that his friend had just played the best tennis of his comeback in Acapulco. When Murray was struggling to keep the ball in court in a hapless exit from Indian Wells last week, Lendl was on the same continent, but not the same page, swapping pleasantries with drunken fans during an exhibition match in Nashville.

Murray said Lendl's absence made no difference. He was just searching for his best tennis, still. The back was fine – but maybe the head was not in such a wonderful place. Through the muted interpretation of a TV screen, Murray looked distracted and resigned, rather than bruised in defeat.

Paradoxically, Lendl's departure coincides with the recent arrival on the coaching scene of two of his contemporaries to guide Murray's rivals: Stefan Edberg, who has helped Federer win in Dubai and reach the final in Indian Wells; and Boris Becker, markedly less successful with Novak Djokovic, who lost to Stanislas Wawrinka in the Australian Open semi-finals and beat Federer in Indian Wells without the German's assistance.

The role of a coach in tennis is ill-defined. There was a time when they were hardly noticed, a time before back-up teams and hi-tech training. Some players, such as Rafael Nadal, rarely contemplate change, and his uncle Toni will almost certainly be there until he retires. They are a comfortable fit and a new voice probably would confuse Nadal.

Murray for years was unsettled. His first mentor as a teenage prodigy was Leon Smith, his Davis Cup captain and mentioned on Wednesdayamong leading candidates in betting speculation about a successor. Mark Petchey took over when Murray joined the Tour, and the door kept revolving until Lendl arrived. The coach said shortly after joining him he could see no reason they would not be together for the rest of the player's career. Murray agreed. Apparently they found a reason.

Lendl will be there in the stands for Murray in Miami. No doubt the player will look up, instinctively, at the man who helped him make history. Lendl might even manage a smile. Or maybe not. Sentiment has never figured in his dealings, although Old Stone Face was not a total lump of rock. "He believed in me when other people didn't," is how Murray put it after he won Wimbledon last summer. He needs another believer, sooner rather than later.